Roman Mani (3)
Hans Herrmann (3)
Ciro Semprebon (1)
Stephan Herminghaus (1)
Capillary forces in assemblies of three spherical particles
B8: Capillary interactions and particle dynamics
10/9/2012 1Siegen, Piko Workshop
(1) Max Planck-Institute for Dynamics and Self-Organizatin, Göttingen, Germany
(2) Experimental Physics, Saarland University, Saarbrücken, Germany
(3) ETH Zurich
Hans Herrmann (3)
Dirk Kadau (3)
Stephan Herminghaus (1)
Martin Brinkmann (1,2)
Zuerich: collective behavior
(contact dynamic simulations)
Goettingen:
Transport phenomena in wet granular assemblies
10/9/2012 2Siegen, Piko Workshop
Stability and capillary forces in clusters:
Beyond the bridge models
Fij
Liquid transport through bridges
Qij
bridge
trimer
pentamer heptamerto
tal liq
uid
surf
ace S
[p
ixel]
tetrahedron
and trimer
liquid volume V [voxel]
tota
l liq
uid
surf
ace S
[p
ixel]
tetrahedronM Scheel et al.
Nature Materials
7: 189 (2008)
10/9/2012 3Siegen, Piko Workshop
capillary forces
• Total force acting on the center of a bead according to parallelogram rule:
• Determine relation between pressure, forces, volume and geometry
(separation distances ) using numerical energy minimization
Force between bead i and j:
Laplace pressure:
No capillary torques on beads if
contact angle hysteresis is absent
10/9/2012 4Siegen, Piko Workshop
Fij sij
Single gap trimer
TrimerDimer
Force at Force at
Trimer Dimer
Force at
contact
Force at
gap
• Force at gap for dimer negligible
• Find two different decay
mechanisms for trimer
10/9/2012 5Siegen, Piko Workshop
Trimer with two gaps, constant volume
Force at gap 02Force at contact 12
Capillary forces in trimer can be well
approximated by pair interactions
• contact betwen bead
1 and 2 ( s12 = 0 )
• bead 0 moving
10/9/2012 6
Other volumes and separations…
s12=0, Vol=0.15 s12=0, Vol=0.2
10/9/2012 7Siegen, Piko Workshop
s12=0, Vol=0.25 S12=0.05, Vol=0.25 s12=0.1, Vol=0.25
With first approximation…
10/9/2012 9Siegen, Piko Workshop
Trimer modeled by a superposition of
“repulsive springs”Symmetric trimers are sufficient
to calculate the coefficients.
s12=s01=s02
Model
Total energy
Modulus of force along a pair of spheres
10/9/2012 10Siegen, Piko Workshop
Coefficients are in general determined
by features of spheres and liquid volume…. Mixing rules
Pressure
Coefficients as function of volume
Offset energySpring constant
10/9/2012 11Siegen, Piko Workshop
Offset separation
Symmetric trimer stability
Checks of the model
Energy numeric
Vol=0.2
Energy model
Vol=0.2
Energy difference
Vol=0.2
10/9/2012 12Siegen, Piko Workshop
Force numeric
Vol=0.2
Force model
Vol=0.2
Force difference
Vol=0.2
Trimer with two gaps, constant pressure
Force at gap 02 Force at contact
12
In case of liquid exchange (pressure as control parameter)
Capillary forces in trimer can be well
approximated by pair interactions
• contact betwen bead
1 and 2 ( s12 = 0 )
• bead 0 moving
10/9/2012 13
Top Related